Problem: Solve for $n$, $ \dfrac{2}{8n} = \dfrac{4n - 4}{4n} + \dfrac{1}{16n} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8n$ $4n$ and $16n$ The common denominator is $16n$ To get $16n$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{2}{8n} \times \dfrac{2}{2} = \dfrac{4}{16n} $ To get $16n$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ \dfrac{4n - 4}{4n} \times \dfrac{4}{4} = \dfrac{16n - 16}{16n} $ The denominator of the third term is already $16n$ , so we don't need to change it. This give us: $ \dfrac{4}{16n} = \dfrac{16n - 16}{16n} + \dfrac{1}{16n} $ If we multiply both sides of the equation by $16n$ , we get: $ 4 = 16n - 16 + 1$ $ 4 = 16n - 15$ $ 19 = 16n $ $ n = \dfrac{19}{16}$